Problem: Michael is 9 years older than Jessica. For the last four years, Michael and Jessica have been going to the same school. Sixteen years ago, Michael was 4 times older than Jessica. How old is Michael now?
Answer: We can use the given information to write down two equations that describe the ages of Michael and Jessica. Let Michael's current age be $m$ and Jessica's current age be $j$ The information in the first sentence can be expressed in the following equation: $m = j + 9$ Sixteen years ago, Michael was $m - 16$ years old, and Jessica was $j - 16$ years old. The information in the second sentence can be expressed in the following equation: $m - 16 = 4(j - 16)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $m$ , it might be easiest to solve our first equation for $j$ and substitute it into our second equation. Solving our first equation for $j$ , we get: $j = m - 9$ . Substituting this into our second equation, we get the equation: $m - 16 = 4($ $(m - 9)$ $ -$ $ 16)$ which combines the information about $m$ from both of our original equations. Simplifying the right side of this equation, we get: $m - 16 = 4m - 100$ Solving for $m$ , we get: $3 m = 84$ $m = 28$.